A310025 Coordination sequence Gal.4.31.2 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

1, 3, 5, 8, 10, 15, 18, 19, 22, 25, 28, 31, 34, 38, 39, 41, 46, 47, 49, 54, 58, 61, 60, 63, 70, 69, 70, 77, 82, 84, 81, 85, 94, 91, 91, 100, 106, 107, 102, 107, 118, 113, 112, 123, 130, 130, 123, 129, 142, 135

Offset

0,2

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

Table of n, a(n) for n=0..49.

Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers

Formula

Conjectures from Chai Wah Wu, Dec 10 2018: (Start)

a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 7*a(n-6) + 8*a(n-7) - 7*a(n-8) + 6*a(n-9) - 5*a(n-10) + 4*a(n-11) - 3*a(n-12) + 2*a(n-13) - a(n-14) for n > 16.

G.f.: (-2*x^16 + 4*x^15 - 3*x^14 + 5*x^13 - 4*x^12 + 11*x^11 - 4*x^10 + 12*x^9 - 2*x^8 + 11*x^7 + 8*x^5 + 2*x^4 + 3*x^3 + 2*x^2 + x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^4 + 1)^2). (End)

Crossrefs

Sequence in context: A190488 A182082 A117467 * A133097 A117176 A212987

Adjacent sequences: A310022 A310023 A310024 * A310026 A310027 A310028

Keyword

nonn

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Status

approved